Multiply the numerator and denominator by the denominator's conjugate (root 3). This gives you 4/3 x root(3) - 3/2 = a + b x root(3), so you equate the rational and irrational coefficients.
Multiply the numerator and denominator by the denominator's conjugate (root 3). This gives you 4/3 x root(3) - 3/2 = a + b x root(3), so you equate the rational and irrational coefficients.